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ON CONTINUOUS AND ADJOINT MORPHISMS BETWEEN NON-COMMUTATIVE PRIME SPECTRA
Published online by Cambridge University Press: 30 May 2006
Abstract
We study topological properties of the correspondence of prime spectra associated with a non-commutative ring homomorphism $R\rightarrow S$. Our main result provides criteria for the adjointness of certain functors between the categories of Zariski closed subsets of $\spec R$ and $\spec S$; these functors arise naturally from restriction and extension of scalars. When $R$ and $S$ are left Noetherian, adjointness occurs only for centralizing and ‘nearly centralizing’ homomorphisms.
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- Copyright © Edinburgh Mathematical Society 2006
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